subsection2
-3.25explus-1ex minus-.2ex
1.5ex plus.2ex
Amdeberhan-type identities

In [1]}
Amdeberhan et al. suggested the conjecture that \(\nu _2(S(2^h+1,k+1))=\nu _2(S(2^h,k))\)  for \(1\le k\le 2^h\) , which was proven by Hong et al. in [2]}. Note that in this range \(S(2^h,k)\)  is a MZC.
A much shorter proof with significant extensions to arbitrary MZ cases and all primes was given by Adelberg in [3]}, using the standard recursion for Stirling numbers of the second kind.
